。
She had a dream that she became a princess.
Literal
She [topic-は] princess [become-に]-became dream [object-を] saw.
夢を見る — literally 'to see a dream' — is the standard idiom for 'to have a dream,' since Japanese conceptualizes dreaming as a visual experience. The relative clause 王女様になった ('became a princess') sits before 夢, with no relative pronoun like English 'that' or 'which' — Japanese simply places the modifying clause directly in front of the noun it modifies. The honorific 様 attached to 王女 ('princess') is a fairy-tale touch: it's the same suffix used for high-status humans (お客様, 神様) and lends storybook formality, common in children's tales and fantasy framing.